Got me stumped. I must say, I am not familiar with TR6 axles, and they are different from Spitfires, so you could have a problem there that I wouldn't know about. Some of the more knowledgeable forum members could maybe help out.
Having said that, its wierd that this noise disappears under acceleration. Wheel bearings generally don't change on acceleration, and as Adam H. says, they will usually get louder on one side or the other on cornering.
Similarly, differential crown/pinion noises usually get louder on acceleration, not quieter. Bearing noise in the diff shouldn't change on acceleration, but it's possible I guess. Have you noticed any oil leaking from around the differential shafts or the pinion seal?
When u-joints wear, they tend to 'knock', not 'hum'. Prop shafts don't usually hum either, they typically vibrate and shake if they're out of balance. And it should get worse as you go faster.
Have you checked simple stuff? Tire treads ok, tire inflation, wheel nuts, etc?
You might also check the differential rubber mounts. Could be you are getting vibration transmitted into the car because they are worn and a little loose, and the torque of acceleration compresses them again. Usually you will get a 'thump' on startup if the rubber mounts are getting worn, though, as the diff twists on startup.
Sorry, that's all I can think of. Hopefully another member will have more experience to share. It will be interesting to see what this turns out to be.